To “supreme” a citrus fruit is to cut away its peel and pith, then remove its segments from between the membranes. It’s a nice technique for fruit salads and sauces; while you lose a bit of the fruit, you don’t get any white pith or fibrous membrane in your dish as you would by simply peeling and sectioning it.
Here’s how: Using a sharp knife, slice the rind off the top and bottom of your fruit, exposing the flesh. Stand the fruit on one end (it’ll now sit flat, for easy paring) and cut the peel and white pith away, going from top to bottom and following the curve of the fruit. Trim away any pith still attached. Hold the fruit in your non-dominant hand, and use a paring knife to cut down one side of a segment, separating it from the membrane. When you get to the bottom, twist the knife up and around the other side of the segment, flipping it out. When you’ve taken all the segments out, squeeze the juice out of the membranes. If you don’t use it in what you’re preparing, you can drink it or save it to use in something else.